Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (2): 736-764.doi: 10.1007/s42967-024-00472-0

• ORIGINAL PAPERS • Previous Articles     Next Articles

Global-Padé Approximation of the Three-Parameter Mittag-Leffler Function: Generalized Derivation and Numerical Implementation Issues

Y. O. Afolabi1, T. A. Biala2, Ibrahim O. Sarumi3,4, B. A. Wade1   

  1. 1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504, USA;
    2. Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN, 37132-0001, USA;
    3. Department of Mathematics, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia;
    4. Interdisciplinary Research Center for Refining and Advanced Chemicals, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia
  • Received:2024-07-03 Revised:2024-11-11 Online:2026-04-07 Published:2026-04-07
  • Contact: Ibrahim O. Sarumi,E-mail:ibrahim.sarumi@kfupm.edu.sa E-mail:ibrahim.sarumi@kfupm.edu.sa

Abstract: In this paper, we discuss a framework for efficient construction of rational approximations for the three-parameter Mittag-Leffler function (MLF) based on the global-Padé approximation technique. Obtaining the coefficients of these approximants is usually the most tedious part in their construction as it requires delicate matching to procure a linear system for these coefficients. The main focus of this paper is the derivation of a novel generalized system that can be used to obtain the coefficients without having to perform the matching task. In particular, we illustrate the use of the generalized system in constructing rational approximants of various degrees subject to choices of feasible parameters. Inequalities providing bounds on permissible choices of these parameters are also obtained. Numerical experiments are conducted to illustrate the accuracy and efficiency of the approximants.

Key words: Prabhakar function, Mittag-Leffler function (MLF), Global rational approximation, Multi-term fractional differential equation, Fractional heat conduction equation

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